You are given an integer array prices where prices[i] is the price of a stock in dollars on the ith day, and an integer k.
You are allowed to make at most k transactions, where each transaction can be either of the following:
Normal transaction: Buy on day i, then sell on a later day j where i < j. You profit prices[j] - prices[i].
Short selling transaction: Sell on day i, then buy back on a later day j where i < j. You profit prices[i] - prices[j].
Note that you must complete each transaction before starting another. Additionally, you can't buy or sell on the same day you are selling or buying back as part of a previous transaction.
Return the maximum total profit you can earn by making at most k transactions.
Example 1:
Input: prices = [1,7,9,8,2], k = 2
Output: 14
Explanation:
We can make $14 of profit through 2 transactions:Example 2:
Input: prices = [12,16,19,19,8,1,19,13,9], k = 3
Output: 36
Explanation:
We can make $36 of profit through 3 transactions:
Constraints:
2 <= prices.length <= 1031 <= prices[i] <= 1091 <= k <= prices.length / 2